EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

CERN-PH-EP-2012-172LHCb-PAPER-2012-013

19 September 2012

Measurement of the effectiveB0

s→ K+K− lifetime

The LHCb collaboration†

Abstract

A precise determination of the effective B0s→ K+K− lifetime can be used to con-

strain contributions from physics beyond the Standard Model in the B0s meson

system. Conventional approaches select B meson decay products that are signifi-cantly displaced from the B meson production vertex. As a consequence, B mesonswith low decay times are suppressed, introducing a bias to the decay time spectrumwhich must be corrected. This analysis uses a technique that explicitly avoids alifetime bias by using a neural network based trigger and event selection. Using1.0 fb−1 of data recorded by the LHCb experiment, the effective B0

s → K+K−

lifetime is measured as 1.455± 0.046 (stat.)± 0.006 (syst.) ps.

Submitted to Physics Letters B.

†Authors are listed on the following pages.

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LHCb collaboration

R. Aaij38, C. Abellan Beteta33,n, A. Adametz11, B. Adeva34, M. Adinolfi43, C. Adrover6,A. Affolder49, Z. Ajaltouni5, J. Albrecht35, F. Alessio35, M. Alexander48, S. Ali38,G. Alkhazov27, P. Alvarez Cartelle34, A.A. Alves Jr22, S. Amato2, Y. Amhis36, J. Anderson37,R.B. Appleby51, O. Aquines Gutierrez10, F. Archilli18,35, A. Artamonov 32, M. Artuso53,35,E. Aslanides6, G. Auriemma22,m, S. Bachmann11, J.J. Back45, V. Balagura28,35, W. Baldini16,R.J. Barlow51, C. Barschel35, S. Barsuk7, W. Barter44, A. Bates48, C. Bauer10, Th. Bauer38,A. Bay36, J. Beddow48, I. Bediaga1, S. Belogurov28, K. Belous32, I. Belyaev28, E. Ben-Haim8,M. Benayoun8, G. Bencivenni18, S. Benson47, J. Benton43, R. Bernet37, M.-O. Bettler17,M. van Beuzekom38, A. Bien11, S. Bifani12, T. Bird51, A. Bizzeti17,h, P.M. Bjørnstad51,T. Blake35, F. Blanc36, C. Blanks50, J. Blouw11, S. Blusk53, A. Bobrov31, V. Bocci22,A. Bondar31, N. Bondar27, W. Bonivento15, S. Borghi48,51, A. Borgia53, T.J.V. Bowcock49,C. Bozzi16, T. Brambach9, J. van den Brand39, J. Bressieux36, D. Brett51, M. Britsch10,T. Britton53, N.H. Brook43, H. Brown49, A. Buchler-Germann37, I. Burducea26, A. Bursche37,J. Buytaert35, S. Cadeddu15, O. Callot7, M. Calvi20,j , M. Calvo Gomez33,n, A. Camboni33,P. Campana18,35, A. Carbone14, G. Carboni21,k, R. Cardinale19,i,35, A. Cardini15, L. Carson50,K. Carvalho Akiba2, G. Casse49, M. Cattaneo35, Ch. Cauet9, M. Charles52, Ph. Charpentier35,P. Chen3,36, N. Chiapolini37, M. Chrzaszcz 23, K. Ciba35, X. Cid Vidal34, G. Ciezarek50,P.E.L. Clarke47, M. Clemencic35, H.V. Cliff44, J. Closier35, C. Coca26, V. Coco38, J. Cogan6,E. Cogneras5, P. Collins35, A. Comerma-Montells33, A. Contu52, A. Cook43, M. Coombes43,G. Corti35, B. Couturier35, G.A. Cowan36, D. Craik45, R. Currie47, C. D’Ambrosio35,P. David8, P.N.Y. David38, I. De Bonis4, K. De Bruyn38, S. De Capua21,k, M. De Cian37,J.M. De Miranda1, L. De Paula2, P. De Simone18, D. Decamp4, M. Deckenhoff9,H. Degaudenzi36,35, L. Del Buono8, C. Deplano15, D. Derkach14,35, O. Deschamps5,F. Dettori39, J. Dickens44, H. Dijkstra35, P. Diniz Batista1, F. Domingo Bonal33,n,S. Donleavy49, F. Dordei11, A. Dosil Suarez34, D. Dossett45, A. Dovbnya40, F. Dupertuis36,R. Dzhelyadin32, A. Dziurda23, A. Dzyuba27, S. Easo46, U. Egede50, V. Egorychev28,S. Eidelman31, D. van Eijk38, F. Eisele11, S. Eisenhardt47, R. Ekelhof9, L. Eklund48,I. El Rifai5, Ch. Elsasser37, D. Elsby42, D. Esperante Pereira34, A. Falabella16,e,14, C. Farber11,G. Fardell47, C. Farinelli38, S. Farry12, V. Fave36, V. Fernandez Albor34, M. Ferro-Luzzi35,S. Filippov30, C. Fitzpatrick47, M. Fontana10, F. Fontanelli19,i, R. Forty35, O. Francisco2,M. Frank35, C. Frei35, M. Frosini17,f , S. Furcas20, A. Gallas Torreira34, D. Galli14,c,M. Gandelman2, P. Gandini52, Y. Gao3, J-C. Garnier35, J. Garofoli53, J. Garra Tico44,L. Garrido33, D. Gascon33, C. Gaspar35, R. Gauld52, N. Gauvin36, E. Gersabeck11,M. Gersabeck35, T. Gershon45,35, Ph. Ghez4, V. Gibson44, V.V. Gligorov35, C. Gobel54,D. Golubkov28, A. Golutvin50,28,35, A. Gomes2, H. Gordon52, M. Grabalosa Gandara33,R. Graciani Diaz33, L.A. Granado Cardoso35, E. Grauges33, G. Graziani17, A. Grecu26,E. Greening52, S. Gregson44, O. Grunberg55, B. Gui53, E. Gushchin30, Yu. Guz32, T. Gys35,C. Hadjivasiliou53, G. Haefeli36, C. Haen35, S.C. Haines44, T. Hampson43,S. Hansmann-Menzemer11, N. Harnew52, S.T. Harnew43, J. Harrison51, P.F. Harrison45,T. Hartmann55, J. He7, V. Heijne38, K. Hennessy49, P. Henrard5, J.A. Hernando Morata34,E. van Herwijnen35, E. Hicks49, M. Hoballah5, P. Hopchev4, W. Hulsbergen38, P. Hunt52,T. Huse49, R.S. Huston12, D. Hutchcroft49, D. Hynds48, V. Iakovenko41, P. Ilten12, J. Imong43,R. Jacobsson35, A. Jaeger11, M. Jahjah Hussein5, E. Jans38, F. Jansen38, P. Jaton36,B. Jean-Marie7, F. Jing3, M. John52, D. Johnson52, C.R. Jones44, B. Jost35, M. Kaballo9,

iii

S. Kandybei40, M. Karacson35, T.M. Karbach9, J. Keaveney12, I.R. Kenyon42, U. Kerzel35,T. Ketel39, A. Keune36, B. Khanji6, Y.M. Kim47, M. Knecht36, O. Kochebina7, I. Komarov29,R.F. Koopman39, P. Koppenburg38, M. Korolev29, A. Kozlinskiy38, L. Kravchuk30,K. Kreplin11, M. Kreps45, G. Krocker11, P. Krokovny31, F. Kruse9, K. Kruzelecki35,M. Kucharczyk20,23,35,j , V. Kudryavtsev31, T. Kvaratskheliya28,35, V.N. La Thi36,D. Lacarrere35, G. Lafferty51, A. Lai15, D. Lambert47, R.W. Lambert39, E. Lanciotti35,G. Lanfranchi18, C. Langenbruch35, T. Latham45, C. Lazzeroni42, R. Le Gac6,J. van Leerdam38, J.-P. Lees4, R. Lefevre5, A. Leflat29,35, J. Lefrancois7, O. Leroy6,T. Lesiak23, L. Li3, Y. Li3, L. Li Gioi5, M. Lieng9, M. Liles49, R. Lindner35, C. Linn11, B. Liu3,G. Liu35, J. von Loeben20, J.H. Lopes2, E. Lopez Asamar33, N. Lopez-March36, H. Lu3,J. Luisier36, A. Mac Raighne48, F. Machefert7, I.V. Machikhiliyan4,28, F. Maciuc10,O. Maev27,35, J. Magnin1, S. Malde52, R.M.D. Mamunur35, G. Manca15,d, G. Mancinelli6,N. Mangiafave44, U. Marconi14, R. Marki36, J. Marks11, G. Martellotti22, A. Martens8,L. Martin52, A. Martın Sanchez7, M. Martinelli38, D. Martinez Santos35, A. Massafferri1,Z. Mathe12, C. Matteuzzi20, M. Matveev27, E. Maurice6, B. Maynard53, A. Mazurov16,30,35,J. McCarthy42, G. McGregor51, R. McNulty12, M. Meissner11, M. Merk38, J. Merkel9,D.A. Milanes13, M.-N. Minard4, J. Molina Rodriguez54, S. Monteil5, D. Moran12,P. Morawski23, R. Mountain53, I. Mous38, F. Muheim47, K. Muller37, R. Muresan26,B. Muryn24, B. Muster36, J. Mylroie-Smith49, P. Naik43, T. Nakada36, R. Nandakumar46,I. Nasteva1, M. Needham47, N. Neufeld35, A.D. Nguyen36, C. Nguyen-Mau36,o, M. Nicol7,V. Niess5, N. Nikitin29, T. Nikodem11, A. Nomerotski52,35, A. Novoselov32,A. Oblakowska-Mucha24, V. Obraztsov32, S. Oggero38, S. Ogilvy48, O. Okhrimenko41,R. Oldeman15,d,35, M. Orlandea26, J.M. Otalora Goicochea2, P. Owen50, B.K. Pal53,J. Palacios37, A. Palano13,b, M. Palutan18, J. Panman35, A. Papanestis46, M. Pappagallo48,C. Parkes51, C.J. Parkinson50, G. Passaleva17, G.D. Patel49, M. Patel50, G.N. Patrick46,C. Patrignani19,i, C. Pavel-Nicorescu26, A. Pazos Alvarez34, A. Pellegrino38, G. Penso22,l,M. Pepe Altarelli35, S. Perazzini14,c, D.L. Perego20,j , E. Perez Trigo34,A. Perez-Calero Yzquierdo33, P. Perret5, M. Perrin-Terrin6, G. Pessina20, A. Petrolini19,i,A. Phan53, E. Picatoste Olloqui33, B. Pie Valls33, B. Pietrzyk4, T. Pilar45, D. Pinci22,R. Plackett48, S. Playfer47, M. Plo Casasus34, F. Polci8, G. Polok23, A. Poluektov45,31,E. Polycarpo2, D. Popov10, B. Popovici26, C. Potterat33, A. Powell52, J. Prisciandaro36,V. Pugatch41, A. Puig Navarro33, W. Qian53, J.H. Rademacker43, B. Rakotomiaramanana36,M.S. Rangel2, I. Raniuk40, G. Raven39, S. Redford52, M.M. Reid45, A.C. dos Reis1,S. Ricciardi46, A. Richards50, K. Rinnert49, D.A. Roa Romero5, P. Robbe7, E. Rodrigues48,51,F. Rodrigues2, P. Rodriguez Perez34, G.J. Rogers44, S. Roiser35, V. Romanovsky32,M. Rosello33,n, J. Rouvinet36, T. Ruf35, H. Ruiz33, G. Sabatino21,k, J.J. Saborido Silva34,N. Sagidova27, P. Sail48, B. Saitta15,d, C. Salzmann37, B. Sanmartin Sedes34, M. Sannino19,i,R. Santacesaria22, C. Santamarina Rios34, R. Santinelli35, E. Santovetti21,k, M. Sapunov6,A. Sarti18,l, C. Satriano22,m, A. Satta21, M. Savrie16,e, D. Savrina28, P. Schaack50,M. Schiller39, H. Schindler35, S. Schleich9, M. Schlupp9, M. Schmelling10, B. Schmidt35,O. Schneider36, A. Schopper35, M.-H. Schune7, R. Schwemmer35, B. Sciascia18, A. Sciubba18,l,M. Seco34, A. Semennikov28, K. Senderowska24, I. Sepp50, N. Serra37, J. Serrano6, P. Seyfert11,M. Shapkin32, I. Shapoval40,35, P. Shatalov28, Y. Shcheglov27, T. Shears49, L. Shekhtman31,O. Shevchenko40, V. Shevchenko28, A. Shires50, R. Silva Coutinho45, T. Skwarnicki53,N.A. Smith49, E. Smith52,46, M. Smith51, K. Sobczak5, F.J.P. Soler48, A. Solomin43,F. Soomro18,35, D. Souza43, B. Souza De Paula2, B. Spaan9, A. Sparkes47, P. Spradlin48,

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F. Stagni35, S. Stahl11, O. Steinkamp37, S. Stoica26, S. Stone53,35, B. Storaci38, M. Straticiuc26,U. Straumann37, V.K. Subbiah35, S. Swientek9, M. Szczekowski25, P. Szczypka36,T. Szumlak24, S. T’Jampens4, M. Teklishyn7, E. Teodorescu26, F. Teubert35, C. Thomas52,E. Thomas35, J. van Tilburg11, V. Tisserand4, M. Tobin37, S. Tolk39, S. Topp-Joergensen52,N. Torr52, E. Tournefier4,50, S. Tourneur36, M.T. Tran36, A. Tsaregorodtsev6, N. Tuning38,M. Ubeda Garcia35, A. Ukleja25, U. Uwer11, V. Vagnoni14, G. Valenti14, R. Vazquez Gomez33,P. Vazquez Regueiro34, S. Vecchi16, J.J. Velthuis43, M. Veltri17,g, M. Vesterinen35, B. Viaud7,I. Videau7, D. Vieira2, X. Vilasis-Cardona33,n, J. Visniakov34, A. Vollhardt37, D. Volyanskyy10,D. Voong43, A. Vorobyev27, V. Vorobyev31, C. Voß55, H. Voss10, R. Waldi55, R. Wallace12,S. Wandernoth11, J. Wang53, D.R. Ward44, N.K. Watson42, A.D. Webber51, D. Websdale50,M. Whitehead45, J. Wicht35, D. Wiedner11, L. Wiggers38, G. Wilkinson52, M.P. Williams45,46,M. Williams50, F.F. Wilson46, J. Wishahi9, M. Witek23, W. Witzeling35, S.A. Wotton44,S. Wright44, S. Wu3, K. Wyllie35, Y. Xie47, F. Xing52, Z. Xing53, Z. Yang3, R. Young47,X. Yuan3, O. Yushchenko32, M. Zangoli14, M. Zavertyaev10,a, F. Zhang3, L. Zhang53,W.C. Zhang12, Y. Zhang3, A. Zhelezov11, L. Zhong3, A. Zvyagin35.

1Centro Brasileiro de Pesquisas Fısicas (CBPF), Rio de Janeiro, Brazil2Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil3Center for High Energy Physics, Tsinghua University, Beijing, China4LAPP, Universite de Savoie, CNRS/IN2P3, Annecy-Le-Vieux, France5Clermont Universite, Universite Blaise Pascal, CNRS/IN2P3, LPC, Clermont-Ferrand, France6CPPM, Aix-Marseille Universite, CNRS/IN2P3, Marseille, France7LAL, Universite Paris-Sud, CNRS/IN2P3, Orsay, France8LPNHE, Universite Pierre et Marie Curie, Universite Paris Diderot, CNRS/IN2P3, Paris, France9Fakultat Physik, Technische Universitat Dortmund, Dortmund, Germany10Max-Planck-Institut fur Kernphysik (MPIK), Heidelberg, Germany11Physikalisches Institut, Ruprecht-Karls-Universitat Heidelberg, Heidelberg, Germany12School of Physics, University College Dublin, Dublin, Ireland13Sezione INFN di Bari, Bari, Italy14Sezione INFN di Bologna, Bologna, Italy15Sezione INFN di Cagliari, Cagliari, Italy16Sezione INFN di Ferrara, Ferrara, Italy17Sezione INFN di Firenze, Firenze, Italy18Laboratori Nazionali dell’INFN di Frascati, Frascati, Italy19Sezione INFN di Genova, Genova, Italy20Sezione INFN di Milano Bicocca, Milano, Italy21Sezione INFN di Roma Tor Vergata, Roma, Italy22Sezione INFN di Roma La Sapienza, Roma, Italy23Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of Sciences, Krakow, Poland24AGH University of Science and Technology, Krakow, Poland25Soltan Institute for Nuclear Studies, Warsaw, Poland26Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest-Magurele, Romania27Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia28Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia29Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow, Russia30Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN), Moscow, Russia31Budker Institute of Nuclear Physics (SB RAS) and Novosibirsk State University, Novosibirsk, Russia32Institute for High Energy Physics (IHEP), Protvino, Russia33Universitat de Barcelona, Barcelona, Spain34Universidad de Santiago de Compostela, Santiago de Compostela, Spain

v

35European Organization for Nuclear Research (CERN), Geneva, Switzerland36Ecole Polytechnique Federale de Lausanne (EPFL), Lausanne, Switzerland37Physik-Institut, Universitat Zurich, Zurich, Switzerland38Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands39Nikhef National Institute for Subatomic Physics and VU University Amsterdam, Amsterdam, TheNetherlands40NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine41Institute for Nuclear Research of the National Academy of Sciences (KINR), Kyiv, Ukraine42University of Birmingham, Birmingham, United Kingdom43H.H. Wills Physics Laboratory, University of Bristol, Bristol, United Kingdom44Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom45Department of Physics, University of Warwick, Coventry, United Kingdom46STFC Rutherford Appleton Laboratory, Didcot, United Kingdom47School of Physics and Astronomy, University of Edinburgh, Edinburgh, United Kingdom48School of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom49Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom50Imperial College London, London, United Kingdom51School of Physics and Astronomy, University of Manchester, Manchester, United Kingdom52Department of Physics, University of Oxford, Oxford, United Kingdom53Syracuse University, Syracuse, NY, United States54Pontifıcia Universidade Catolica do Rio de Janeiro (PUC-Rio), Rio de Janeiro, Brazil, associated to 2

55Institut fur Physik, Universitat Rostock, Rostock, Germany, associated to 11

aP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS), Moscow, RussiabUniversita di Bari, Bari, ItalycUniversita di Bologna, Bologna, ItalydUniversita di Cagliari, Cagliari, ItalyeUniversita di Ferrara, Ferrara, ItalyfUniversita di Firenze, Firenze, ItalygUniversita di Urbino, Urbino, ItalyhUniversita di Modena e Reggio Emilia, Modena, ItalyiUniversita di Genova, Genova, ItalyjUniversita di Milano Bicocca, Milano, ItalykUniversita di Roma Tor Vergata, Roma, ItalylUniversita di Roma La Sapienza, Roma, ItalymUniversita della Basilicata, Potenza, ItalynLIFAELS, La Salle, Universitat Ramon Llull, Barcelona, SpainoHanoi University of Science, Hanoi, Viet Nam

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1 Introduction

The study of charmless b-hadron decays can be used to explore the phase structure of theCKM matrix and to search for indirect evidence of physics beyond the Standard Model(SM). A measurement of the effective lifetime of the B0

s→ K+K− decay (charge conjugatemodes are implied throughout) is of considerable interest as it is sensitive to new physicalphenomena affecting the B0

s mixing phase and entering the decay at loop level [1–4].The B0

s→ K+K− decay was first observed by the CDF collaboration [5] and the mostprecise measurement to date of the effective lifetime was made by the LHCb collaborationusing data taken during 2010 [6]. A detailed theoretical description of the B0

s→ K+K−

decay can be found in Refs. [3, 4]. When the initial flavour of the B0s meson is unknown

the decay time distribution can be written as

Γ(t) ∝ (1−A∆Γs) e−ΓLt + (1 +A∆Γs) e

−ΓH t. (1)

The quantities ΓH and ΓL are the decay widths of the heavy and light B0s mass eigenstates

and ∆Γs = ΓL − ΓH is the decay width difference. The parameter A∆Γs is defined asA∆Γs = −2Re(λ)/ (1 + |λ|2) where λ = (q/p)(A/A), where the complex coefficients p andq define the mass eigenstates of the B0

s–B0s system in terms of the flavour eigenstates (see

e.g., Ref. [7]) and A (A) is the amplitude for a B0s (B0

s) meson to decay to the K+K−

final state.If the decay time distribution given by Eq. 1 is fitted with a single exponential function

the effective lifetime is given by [8]

τKK =τB0

s

1− y2s

[1 + 2A∆Γsys + y2

s

1 +A∆Γsys

]= τB0

s

(1 +A∆Γsys +O(y2

s)), (2)

where τB0s

= 2/ (ΓH + ΓL) = Γ−1s and ys = ∆Γs/2Γs. The K+K− final state is CP -

even and so in the SM the decay is dominated by the light mass eigenstate such thatA∆Γs = −0.972±0.012 [3,9] and the effective lifetime thus is approximately equal to Γ−1

L .Adopting the approach of Ref. [3] and using the world averages of Γs and ∆Γs [10] andthe SM prediction of A∆Γs , the effective lifetime is predicted to be τKK = 1.40± 0.02 ps.However, the B0

s→ K+K− decay is dominated by penguin diagrams and so is sensitive tophysics beyond the SM entering at loop level, which may affect A∆Γs . The measurementis also sensitive to new physics contributions to the B0

s mixing phase which in turn affects∆Γs [11]. Deviations from this prediction will therefore provide evidence of new physics.

Conventional selections exploit the long lifetimes of b-hadrons by requiring that theirdecay products are significantly displaced from the primary interaction point. However,this introduces a time-dependent acceptance of the selected b-hadron candidates whichneeds to be taken into account in the analysis. This paper describes a technique basedon neural networks which avoids such acceptance effects. Only properties independentof the decay time are used to discriminate between signal and background. To exploitthe available information, including the correlations between variables, several neuralnetworks are used in a dedicated trigger and event selection.

1

2 The LHCb experiment and simulation software

The B0s → K+K− lifetime is measured using 1.0 fb−1 of pp collision data collected by

the LHCb detector at a centre of mass energy of√s = 7 TeV during 2011. The LHCb

detector [12] is a single arm spectrometer with a pseudorapidity acceptance of 2 < η < 5for charged particles. The detector includes a high precision tracking system, whichconsists of a silicon vertex detector and dedicated tracking planes. The tracking planesconsist of silicon microstrip detectors in the region with high charged-particle flux closeto the beam pipe and straw tube detectors which provide coverage up to the edge of theLHCb geometrical acceptance. The tracking planes are located either side of the dipolemagnet to allow the measurement of the momenta of charged particles as they traverse thedetector. Excellent particle identification capabilities are provided by two ring imagingCherenkov detectors which allow charged pions, kaons and protons to be distinguishedfrom each other in the momentum range 2–100 GeV/c. The energy of particles traversingthe detector is measured using a calorimeter system which is sensitive to photons andelectrons, as well as hadrons. Muons are identified using a dedicated detector system.

The experiment employs a multi-level trigger comprised of a hardware trigger whichuses information from the calorimeter and muon system and a software trigger whichperforms a full reconstruction of the event, including tracks and vertices.

The simulated events used in this analysis are produced using the Pythia 6.4 genera-tor [13], with a choice of parameters specifically configured for LHCb [14]. The EvtGenpackage [15] describes the decay of b-hadrons and the Geant4 toolkit [16] simulates thedetector response, implemented as described in Ref. [17]. QED radiative corrections tothe B0

s→ K+K− decay are generated with the Photos package [18].sectionTrigger and event selection At LHCb, b-hadrons are produced with an average

momentum of around 100 GeV/c and have decay vertices displaced from the primaryinteraction vertex. Combinatorial background candidates, produced by the random com-bination of tracks, tend to have low momentum and originate from a primary pp collisionvertex. These features are typically exploited to select b-hadrons and reject background.The distance of closest approach (impact parameter) of b-hadron decay products to anyprimary vertex is a particularly important discriminant in the trigger because it is anorder of magnitude faster to compute than the momenta of the same decay products.For this reason, the majority of triggers for hadronic b-hadron decays begin by selectingtracks with a significant displacement from any primary vertex. However, such require-ments introduce a time-dependent acceptance which biases the decay time distribution ofthe selected b-hadron candidates and a significant investment of effort is often required tocorrect for this bias.

The analysis presented here uses an approach that selects b-hadrons without bias-ing the decay time distribution, other than trivially through a simple minimum decaytime requirement, limiting the systematic uncertainties associated with correcting for anytime-dependent acceptance effects. This is achieved using neural networks based on theNeuroBayes package [19] in the software trigger and event selection. Neural networkshave advantages over traditional “cut-based” approaches since they are able to exploit

2

the correlations between variables in order to increase signal purity, allowing b-hadronsto be selected without resorting to requirements on impact parameters or flight distance.

The LHCb software trigger has two stages which run sequentially. Due to restrictionson processing time it is not possible to employ a neural network in the first level of thesoftware trigger. Instead, only tracks that are not used in the first level decision are passedto the second trigger level in order to avoid a potential bias. These tracks are required topass a loose pre-selection with requirements on their momenta, transverse momenta andtrack fit quality. The tracks are then combined to form B meson candidates, using a kaonmass hypothesis for both tracks, and further requirements are made on the distance ofclosest approach of the two tracks to each other, the mass of the resulting candidate, thehelicity angle of the tracks in the B meson rest frame and the quality of the decay vertexfit.

After this pre-selection the candidates pass through a first neural network, trained onsimulated B0

s → K+K−, B0→ K+π− and background events, which uses the momentaand transverse momenta of the tracks and B meson candidate, the distance of closestapproach of the two tracks, helicity angle, the χ2 of the vertex fit and the uncertaintyon the fitted B meson mass to discriminate between signal and background. After thisstage the data rate is reduced to a level such that each event may be fully reconstructed,including information from the particle identification system. A second network, trainedon the same simulated events, uses the information presented to the first network alongwith particle identification information to further increase the purity of B mesons in theselected candidates.

Roughly half way through 2011 the luminosity delivered by the LHC accelerator in-creased to a level such that it was necessary to require that the decay time of B mesoncandidates exceeded 0.3 ps in order to keep the trigger rate within acceptable limits. Thisrequirement only biases the decay time distribution in a trivial way, except through apossible difference in the decay time resolutions of the trigger and offline reconstructionsoftware.

After the trigger, the tracks associated to the selected candidates are removed fromthe primary vertex fit to avoid a potential bias in the measured decay time. The purity ofsignal candidates is then further enhanced using two additional sequential neural networks.The first network is trained using simulated events and combines the same informationused by the trigger networks along with particle identification information, the energyof each track from the calorimeter, the probability that either track is formed from theassociation of random hits in the detector and the χ2 per degree of freedom for both trackfits. This network benefits from the more detailed full event reconstruction which is notavailable in the trigger.

The second network is trained on the data recorded in 2011 using sWeights [20],which are calculated in a window around the signal peak and in the upper sidebandregion (5.45 < mK+K− < 5.85 GeV/c2) of the invariant mass spectrum. The sWeightsare obtained from a fit to the invariant mass spectrum of the candidates and the neuralnetwork uses them to discriminate between signal and background. This network usesthe output of the first network as input, all the input variables used by the first network,

3

the uncertainty on the decay time of the B meson candidate and the impact parameter ofthe B meson candidate with respect to the primary interaction vertex. Only candidateswith a decay time of τ > 0.3 ps are used in the network training.

The event selection is determined by making a requirement on the output of this secondneural network that maximises the metric s/

√s+ b, where s is the number of signal

decays in the region 5.05 < mK+K− < 5.85 GeV/c2 and b is the number of backgroundcombinations.

The trigger and offline software reconstruct B meson decay times with different reso-lutions. Potential “edge-effects” introduced by the trigger requirement that τ > 0.3 ps areavoided by requiring that candidates satisfy τ > 0.5 ps in the final event selection. Thecontribution from the B0→ K+π− and B0

s→ K+K− modes are separated by demandingtight requirements on the particle identification properties of the final state particles. Asmall level of contamination from decays of Λb baryons is further suppressed by demandingthat the final state particles are not compatible with the proton hypothesis.

3 Analysis of the effective B0s → K+K− lifetime

The effective B0s → K+K− lifetime is evaluated using an unbinned log-likelihood fit. A

fit to the invariant mass spectrum is performed to determine the sWeights that are usedto isolate the B0

s → K+K− decay time distribution from the residual background. TheB0

s → K+K− signal component is described by a Gaussian function. The backgroundcontamination from partially reconstructed B meson decays is described by a furtherGaussian function and the combinatorial background is described by a Chebychev poly-nomial with one free parameter. It should be noted that the kaon mass is assigned to bothfinal state particles in the vertex fit and hence the reconstructed B0→ K+π− mass isshifted towards higher values than the nominal mass, creating an asymmetric distribution.The B0→ K+π− signal component is therefore described by a Crystal Ball function [21]with the tail on high mass side. The parameters of this distribution are fixed using a fit tothe independent B0→ K+π− sample, separated using particle identification information.

The fit finds 997 ± 34 B0s → K+K− decays and 78 ± 17 B0→ K+π− decays in the

data with 253 ± 25 and 169 ± 20 combinatorial background and partially reconstructedcombinations respectively. Figure 1(a) shows the resulting invariant mass spectrum forB0

s→ K+K− candidates.Using the sWeights returned by the mass fit, the B0

s→ K+K− decay time distributionis extracted from data using the sPlot technique [20]. Since there is no acceptance biasto correct for, the lifetime is determined using a fit of the convolution of an exponentialand Gaussian function to account for the resolution of the detector. The mean of theGaussian function is fixed to zero and its width is fixed to the expected resolution fromsimulated events, which is σt = 0.04 ps.

The effective B0s→ K+K− lifetime is found to be

τKK = 1.455± 0.046 (stat.) ps.

4

]2 [GeV/c-K+Km5.2 5.4 5.6 5.8

2C

andi

date

s / 8

MeV

/c

0

20

40

60

80

100

120

140

160

180

LHCbData

- K+ K→s0B

-π + K→0B

Partially reconstructed

Comb. back.

(a)

Decay time [ps]2 4 6 8 10 12sW

eigh

ted

cand

idat

es /

0.25

ps

-110

1

10

210 LHCb (b)

Figure 1: (a) Invariant mass spectrum for all selected B0s → K+K− candidates. (b)

Decay time distribution of B0s → K+K− signal extracted using sWeights and the fitted

exponential function.

Figure 1(b) shows the corresponding fit to the decay time distribution of B0s → K+K−

signal.Since the decay B0→ K+π− has similar kinematics, it can be used as a control mode.

However, since the kaon mass hypothesis is assigned to both tracks, the measured decaytime is biased to larger values for B0→ K+π−. To avoid this bias a fit is made to thereduced decay time, which is defined as the decay time divided by the invariant mass. Thisquantity is independent of the mass assigned to the two tracks and is also unbiased by theselection, following an exponential distribution with decay constant equal to mB0/τB0 .

Using the value of the B0 mass [7] as input, the B0 lifetime is found to be

τB0 = 1.536± 0.031 (stat.) ps

which agrees with the current world-average τB0 = 1.519± 0.007 ps [7].

4 Evaluation of systematic uncertainties

A wide range of effects that can influence the measurement of the effective B0s→ K+K−

lifetime has been evaluated. The individual contributions to the systematic uncertaintiesare described below and their estimated values are summarised in Table 1.

The key principle of this analysis is that the trigger and event selection do not biasthe decay time distribution of the selected B0

s → K+K− candidates other than in atrivial way through a minimum decay time requirement. This has been tested extensivelyusing simulated events at each stage of the selection process to demonstrate that no stepintroduces a time-dependent acceptance. Figure 2 shows the efficiency of the full triggerand event selection as a function of decay time for simulated B0

s→ K+K− candidates. Thegraph is fitted with a first order polynomial with a gradient of −0.09±0.30 ns−1 consistent

5

with a uniform acceptance. Possible discrepancies between simulated and real events areconsidered by comparing the distributions of variables used by the neural networks andgood agreement is observed. The available quantity of simulated events limits any non-zero gradient in the acceptance to within 0.30 ns−1. This limit is used to evaluate theshift in the measured effective lifetime due to the presence of a linear acceptance and anegligible deviation is observed and is not considered any further.

Decay time [ps]2 4 6 8 10

Eff

icie

ncy

0.00

0.05

0.10

0.15

0.20

LHCb simulation

Figure 2: Combined efficiency of LHCb trigger, selection neural networks and particleidentification requirements as a function of decay time for simulated B0

s→ K+K− signalcandidates.

Studies using simulated events have demonstrated that the efficiency with which tracksare reconstructed decreases as the impact parameter of the track with respect to thebeam line (IPz) increases. This introduces a decay time acceptance that may bias themeasured lifetime. Such a systematic bias has been evaluated using a combination ofdata and simulated events. First, the effective lifetime of simulated B0

s→ K+K− signalcandidates is found after reconstruction to deviate by 5 fs from the generated value.Second, the tracking efficiency is parametrised as a function of IPz using simulated events.The calculated efficiency is then applied as a weight to events in data according to theirIPz values and the effective lifetime is evaluated. This produces a deviation of 4 fs withrespect to the unweighted events. The larger of these two shifts is taken as the systematicuncertainty introduced by the reconstruction acceptance.

The invariant mass distribution of B0s → K+K− signal candidates is modelled using

a Gaussian function. Potential systematic effects due to this parametrisation are evalu-ated by using the sum of two Gaussian functions to model additional resolution effectsand separately a Crystal Ball function [21] to model final state radiation. Additionallythe background parametrisation is checked by replacing the first order Chebychev poly-nomial with an exponential function. All these changes shift the measured lifetime byapproximately 1 fs which is taken as the systematic uncertainty.

The decay time distribution is fitted with an exponential function convolved with

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a Gaussian function to model detector resolution, where the resolution is fixed to thevalue obtained from simulated events. As a cross-check, the fit is performed with theresolution parameter allowed to vary and also using a simple exponential function withoutattempting to model detector resolution. No deviation from the default measurement ofthe effective lifetime is observed in either case.

The effective B0s → K+K− lifetime measurement has been evaluated using an al-

ternative method which makes a simultaneous fit to the invariant mass and decay timedistributions. This approach requires a parametrisation of the background decay time dis-tribution since the sPlot technique is not used. Both methods give equivalent numericalresults.

A wide range of different approaches to the training of the neural network have beentested, as well as the influence of different alignment and calibration settings and thenumber of simultaneous primary interactions in the detector. All results obtained inthese checks are consistent with the result of the default analysis.

The measured decay times of B meson candidates are determined from the distancebetween the primary interaction and the secondary decay vertex in the silicon vertexdetector. A systematic bias may therefore be introduced due to uncertainty on the LHCblength scale. This effect is estimated by considering the uncertainty on the length scalefrom the mechanical survey, thermal expansion and the current alignment precision. Theuncertainty on the length of the detector along the beam-line is determined to be thedominant effect and a corresponding systematic uncertainty is assigned.

The effective lifetime is obtained by fitting a single exponential function to the dis-tribution given by Eq. 1. However, the requirement that the decay time be greater than0.5 ps diminishes the ΓL component relative to the ΓH component in the decay time dis-tribution. This effect has been evaluated using simulated events and a deviation of 1 fsfrom the result of a fit to the full decay time range is observed.

If the production rates, R, of B0s and B0

s mesons are not equal then an additionaloscillatory term is introduced into the decay time distribution given in Eq. 1, proportionalto the production asymmetry AP ≡

[R(B0

s)−R(B0s )]/[R(B0

s) +R(B0s )]. This term may

alter the measured effective lifetime. Since the B0s meson shares no valence quarks with

the proton AP (B0s ) at LHCb is expected to be small. Making the conservative assumption

that the |AP (B0s )| = |AP (B0)| = 0.01 [22] we find a shift from the expected value of the

effective lifetime of 2 fs using simulated events. This value is assigned as the systematicuncertainty.

5 Conclusions

Two-body charmless B decays offer a rich phenomenology to explore the phase structureof the CKM matrix and to search for manifestations of physics beyond the SM. Theeffective lifetime of the decay B0

s→ K+K− is of considerable theoretical interest as it issensitive to new particles entering at loop level. A measurement of this quantity is madepossible by the excellent particle identification capabilities of the LHCb experiment.

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Table 1: Contributions to the systematic uncertainty on the effective B0s→ K+K− lifetime

measurement. The total uncertainty is calculated by adding the individual contributionsin quadrature.

Systematic sources Uncertainty on τKK [fs]Reconstruction efficiency 5Signal model 1Background model 1Length scale 1Minimum decay time requirement 1Production asymmetry 2Total 6

The effective lifetime of the decay mode B0s→ K+K− is measured using 1.0 fb−1 of

data recorded by the LHCb detector in 2011. A key element of this analysis is that thetrigger and event selection selects B mesons without biasing the decay time distribution.This is achieved using a series of neural networks. Although this dedicated trigger has alower efficiency compared to the one used in the previous LHCb measurement [6], it hasthe advantage of avoiding systematic uncertainties related to the depletion of candidatesat low decay times and provides an independent approach to measuring the B0

s→ K+K−

effective lifetime. It is measured as

τKK = 1.455± 0.046 (stat.)± 0.006 (syst.) ps,

in good agreement with the SM prediction of 1.40±0.02 ps and with the measurement ondata recorded by LHCb in 2010 of 1.440±0.096 (stat.)±0.008 (syst.)±0.003 (mod.) ps [6].

Acknowledgements

We express our gratitude to our colleagues in the CERN accelerator departments forthe excellent performance of the LHC. We thank the technical and administrative staff atCERN and at the LHCb institutes, and acknowledge support from the National Agencies:CAPES, CNPq, FAPERJ and FINEP (Brazil); CERN; NSFC (China); CNRS/IN2P3(France); BMBF, DFG, HGF and MPG (Germany); SFI (Ireland); INFN (Italy); FOMand NWO (The Netherlands); SCSR (Poland); ANCS (Romania); MinES of Russia andRosatom (Russia); MICINN, XuntaGal and GENCAT (Spain); SNSF and SER (Switzer-land); NAS Ukraine (Ukraine); STFC (United Kingdom); NSF (USA). We also acknowl-edge the support received from the ERC under FP7 and the Region Auvergne.

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